Meanwhile, in 12-inch skillet over medium-high heat, in hot olive or salad oil, cook mushrooms and onion until golden and tender. Stir in garlic, zucchini, and carrot; cook until vegetables are tender-crisp. Stir in clams with their liquid, 1/4 teaspoon salt, and 1/2 cup water; over high heat, heat to boiling. Remove skillet from heat; stir in 1/4 cup grated Parmesan cheese.

Drain linguine. Place linguine on large platter; top with vegetable mixture. Toss before serving. If you like, serve with Parmesan cheese.